📚 Year 12 OCR Chemistry: Formula and Theorem Quick Reference Handbook | OCR 化学公式定理速查手册
Mastering the essential formulas and key theorems is the backbone of success in Year 12 OCR Chemistry. This handbook brings together all the quantitative relationships, thermodynamic principles, and structural rules you need to recall quickly — from the mole concept to VSEPR, from enthalpy cycles to equilibrium constants. Each section is designed for rapid revision, pairing clear chemical equations with concise explanations so you can find the right tool for any calculation or concept question.
掌握核心公式与重要定理是学好 Year 12 OCR 化学的基石。这本速查手册汇集了所有你需要记住的定量关系、热力学原理和结构规则——从摩尔概念到价层电子对互斥理论，从焓循环到平衡常数。每个小节专为快速复习设计，将清晰的化学方程与简洁的解释配对呈现，帮助你为任何计算或概念题迅速找到合适的工具。
1. The Mole and Molar Mass | 摩尔与摩尔质量
The mole (mol) is the SI unit for amount of substance. One mole contains exactly 6.02214076 × 10²³ elementary entities (Avogadro constant, NA).
摩尔（mol）是物质的量的国际单位。1 摩尔恰好含有 6.02214076 × 10²³ 个基本单元（阿伏伽德罗常数，NA）。
The fundamental relationship is: n = m / M, where n is amount in mol, m is mass in g, and M is molar mass in g mol⁻¹.
基本关系为：n = m / M，其中 n 为物质的量（mol），m 为质量（g），M 为摩尔质量（g mol⁻¹）。
Molar mass M is numerically equal to the relative atomic mass Ar or relative formula mass Mr, but has units g mol⁻¹.
摩尔质量 M 在数值上等于相对原子质量 Ar 或相对式量 Mr，但单位为 g mol⁻¹。
To find the number of particles: Number of particles = n × NA.
求粒子数：粒子数 = n × NA。
2. Concentration, Volume and Titration | 浓度、体积与滴定
Concentration of a solution is the amount of solute dissolved in a given volume: c = n / V, where c is concentration (mol dm⁻³), n is amount (mol), and V is volume of solution (dm³).
溶液浓度是指溶解在单位体积中的溶质的量：c = n / V，其中 c 为浓度（mol dm⁻³），n 为物质的量（mol），V 为溶液体积（dm³）。
Often concentration is also expressed in g dm⁻³: Concentration (g dm⁻³) = mass (g) / volume (dm³).
浓度也常用 g dm⁻³ 表示：浓度（g dm⁻³）= 质量（g）/ 体积（dm³）。
In a titration, the reaction ratio from the balanced equation allows calculation of unknown concentrations: nacid / nbase = stoichiometric ratio. The simple formula for monoprotic acid and base is caVa / cbVb = a / b, but it is safer to use amounts.
在滴定中，根据配平方程式的反应比可以计算未知浓度：n酸 / n碱 = 化学计量比。对于一元酸和一元碱，简化公式为 caVa / cbVb = a / b，但使用物质的量计算更可靠。
3. Empirical and Molecular Formulae | 实验式与分子式
The empirical formula gives the simplest whole-number ratio of atoms of each element in a compound. It is found by converting % by mass (or mass) to moles, then dividing by the smallest number of moles to obtain a ratio.
实验式表示化合物中各元素原子数目最简单的整数比。求法是先将质量（或质量百分数）转换为摩尔数，再除以其中最小的摩尔数，得到最简整数比。
The molecular formula shows the actual number of atoms of each element in a molecule. It is a whole-number multiple of the empirical formula: Molecular formula = (Empirical formula) × Mr / (mass of empirical formula).
分子式表示一个分子中各元素的实际原子数目，是实验式的整数倍：分子式 = (实验式) × Mr / (实验式质量)。
For example, glucose has empirical formula CH₂O and molecular formula C₆H₁₂O₆ because its Mr is 180 and the empirical mass is 30, giving a multiplier of 6.
例如，葡萄糖的实验式为 CH₂O，分子式为 C₆H₁₂O₆，因为其 Mr 为 180，实验式质量为 30，倍数为 6。
4. Gas Calculations and the Ideal Gas Equation | 气体计算与理想气体方程
At room temperature and pressure (RTP, 20 °C and 101 kPa), one mole of any ideal gas occupies 24.0 dm³. Therefore: n = V (dm³) / 24.0 or V = n × 24.0.
在常温常压下（RTP，20 °C，101 kPa），1 mol 任何理想气体占有的体积为 24.0 dm³。因此：n = V（dm³）/ 24.0 或 V = n × 24.0。
The ideal gas equation relates pressure, volume, temperature and amount for any gas: pV = nRT.
理想气体方程关联了气体的压力、体积、温度和物质的量：pV = nRT。
Units must be consistent: p in Pa, V in m³, n in mol, T in K, R = 8.314 J mol⁻¹ K⁻¹. To convert: 1 kPa = 1000 Pa, 1 dm³ = 1 × 10⁻³ m³, T/K = θ/°C + 273.
使用时必须单位统一：p 用 Pa，V 用 m³，n 为 mol，T 用 K，R = 8.314 J mol⁻¹ K⁻¹。换算关系：1 kPa = 1000 Pa，1 dm³ = 1 × 10⁻³ m³，T/K = θ/°C + 273。
The equation can be rearranged to find molar mass: M = mRT / pV, where m is the mass of gas.
该方程可变形求摩尔质量：M = mRT / pV，其中 m 为气体质量。
5. Yield and Atom Economy | 产率与原子经济
Percentage yield compares the actual mass of product obtained to the theoretical mass expected from stoichiometry: % yield = (actual yield / theoretical yield) × 100.
百分产率将实际获得的产品质量与根据化学计量关系预期得到的理论质量进行比较：% 产率 = (实际产量 / 理论产量) × 100。
Atom economy measures how efficiently reactant atoms end up in the desired product: % atom economy = (Mr of desired product / sum of Mr of all reactants) × 100.
原子经济性衡量反应物原子被利用到目标产物中的效率：% 原子经济 = (目标产物 Mr / 所有反应物 Mr 之和) × 100。
High atom economy is preferred in green chemistry because it reduces waste. Addition reactions tend to have 100% atom economy, whereas substitution and elimination reactions typically have lower atom economy.
绿色化学追求高原子经济性，因为它可以减少废物。加成反应往往可达 100% 原子经济，而取代和消除反应通常原子经济较低。
6. Enthalpy Changes and Calorimetry | 焓变与量热法
Enthalpy change ΔH is the heat energy transferred in a reaction at constant pressure, measured in kJ mol⁻¹. Exothermic reactions have negative ΔH, endothermic have positive ΔH.
焓变 ΔH 是恒压下反应中转移的热量，单位为 kJ mol⁻¹。放热反应 ΔH 为负值，吸热反应为正值。
In a calorimetry experiment, heat transferred is calculated using: q = mcΔT, where q is heat energy (J), m is mass of water/solution (g), c is specific heat capacity (4.18 J g⁻¹ K⁻¹ for water), and ΔT is temperature change (K or °C).
在量热实验中，传递的热量用 q = mcΔT 计算，其中 q 为热量（J），m 为水或溶液质量（g），c 为比热容（水为 4.18 J g⁻¹ K⁻¹），ΔT 为温度变化（K 或 °C）。
Then the enthalpy change per mole is: ΔH = −q / n (negative sign because ΔH is negative for exothermic reaction if temperature rose). Ensure q is in kJ by dividing by 1000.
然后每摩尔的焓变为：ΔH = −q / n（负号是因为温度升高对应放热反应，ΔH 为负）。注意将 q 转换为 kJ，即除以 1000。
Standard enthalpy changes (ΔH°) refer to standard conditions: 100 kPa, 298 K, solutions at 1 mol dm⁻³. Common types include ΔfH° (formation), ΔcH° (combustion), ΔrH° (reaction), ΔneutH° (neutralisation).
标准焓变（ΔH°）指在标准条件下：100 kPa，298 K，溶液浓度 1 mol dm⁻³。常见类型包括 ΔfH°（生成焓）、ΔcH°（燃烧焓）、ΔrH°（反应焓）、ΔneutH°（中和焓）。
7. Hess’s Law and Bond Enthalpies | 赫斯定律与键能
Hess’s Law states that the total enthalpy change of a reaction is independent of the route taken, provided initial and final conditions are the same. This allows ΔH to be calculated using enthalpy cycles from formation or combustion data.
赫斯定律指出，只要始态和终态相同，反应的总焓变与路径无关。利用该定律可用生成焓或燃烧焓数据构建焓循环来计算 ΔH。
Using standard enthalpies of formation: ΔH° = Σ ΔfH° (products) − Σ ΔfH° (reactants).
使用标准生成焓：ΔH° = Σ ΔfH°（产物）− Σ ΔfH°（反应物）。
Using standard enthalpies of combustion: ΔH° = Σ ΔcH° (reactants) − Σ ΔcH° (products).
使用标准燃烧焓：ΔH° = Σ ΔcH°（反应物）− Σ ΔcH°（产物）。
Mean bond enthalpies can also estimate ΔH: ΔH ≈ Σ E(bonds broken) − Σ E(bonds made). This is less accurate because bond enthalpies are average values and do not account for intermolecular forces or environment.
平均键能也可估算 ΔH：ΔH ≈ Σ E(断裂的键) − Σ E(生成的键)。此方法精度较低，因为键能是平均值，未考虑分子间作用力或化学环境。
8. The Equilibrium Constant Kc | 平衡常数 Kc
For a reversible reaction at dynamic equilibrium, the equilibrium constant Kc is defined in terms of concentrations: for aA + bB ⇌ cC + dD, Kc = [C]ᶜ [D]ᵈ / [A]ᵃ [B]ᵇ, where square brackets denote equilibrium concentrations in mol dm⁻³.
对于处于动态平衡的可逆反应，平衡常数 Kc 以浓度定义：对于 aA + bB ⇌ cC + dD，Kc = [C]ᶜ [D]ᵈ / [A]ᵃ [B]ᵇ，方括号表示平衡浓度，单位为 mol dm⁻³。
Kc is constant only at a given temperature. Changing concentration or pressure does not alter Kc, but temperature changes do: for an exothermic forward reaction, increasing temperature decreases Kc; for endothermic, Kc increases.
Kc 仅在一定温度下为常数。改变浓度或压力不会改变 Kc，但温度改变会影响它：若正向反应放热，升高温度会使 Kc 减小；若吸热，则 Kc 增大。
The magnitude of Kc indicates the position of equilibrium: Kc >> 1 means products are favoured, Kc << 1 means reactants are favoured.
Kc 的大小指示平衡位置：Kc >> 1 表示产物占优势，Kc << 1 表示反应物占优势。
9. Rate of Reaction | 反应速率
The rate of a reaction is defined as the change in concentration of a reactant or product per unit time: Rate = Δ[A] / Δt, with units usually mol dm⁻³ s⁻¹. For a reactant disappearing, a negative sign is often used: Rate = −Δ[R]/Δt.
反应速率定义为单位时间内反应物或产物浓度的变化：速率 = Δ[A] / Δt，单位通常为 mol dm⁻³ s⁻¹。对于消耗的反应物，常用负号：速率 = −Δ[R]/Δt。
Collision theory: for a reaction to occur, particles must collide with the correct orientation and with energy greater than or equal to the activation energy Ea.
碰撞理论：发生反应需要粒子以正确的取向碰撞，且能量必须大于或等于活化能 Ea。
Factors affecting rate include concentration (or pressure for gases), temperature, surface area of solid reactants, and the presence of a catalyst. A catalyst provides an alternative reaction pathway with lower Ea, increasing the fraction of successful collisions.
影响速率的因素有：浓度（或气体分压）、温度、固体反应物的表面积以及催化剂的使用。催化剂提供一条活化能 Ea 较低的反应路径，从而增加了有效碰撞的比例。
For the OCR specification, Year 12 students should be able to interpret rate-concentration graphs from experimental data, but the rate equation (rate = k[A]ᵐ[B]ⁿ) and orders of reaction are mainly covered in Year 13.
对于 OCR 考纲，Year 12 学生应能解读实验数据得出的速率-浓度图，但速率方程（rate = k[A]ᵐ[B]ⁿ）及反应级数主要在 Year 13 涉及。
10. Shapes of Molecules (VSEPR) | 分子形状（价层电子对互斥理论）
Valence Shell Electron Pair Repulsion (VSEPR) theory states that electron pairs around a central atom arrange themselves to minimise repulsion, determining molecular shape. The order of repulsion is: lone pair-lone pair > lone pair-bond pair > bond pair-bond pair.
价层电子对互斥理论（VSEPR）认为，中心原子周围的电子对会自行排列以最小化排斥作用，从而决定分子形状。排斥力大小顺序为：孤对-孤对 > 孤对-键对 > 键对-键对。
Key shapes to remember for Year 12:
以下 Year 12 需要记住的关键形状：
| Bonding pairs / 键对 | Lone pairs / 孤对 | Shape / 形状 | Bond angle / 键角 | Example / 例子 |
|---|---|---|---|---|
| 2 | 0 | Linear / 直线形 | 180° | BeCl₂, CO₂ |
| 3 | 0 | Trigonal planar / 三角形 | 120° | BF₃, SO₃ |
| 4 | 0 | Tetrahedral / 四面体形 | 109.5° | CH₄, NH₄⁺ |
| 3 | 1 | Trigonal pyramidal / 三角锥形 | 107° | NH₃ |
| 2 | 2 | Bent / V 形 | 104.5° | H₂O |
| 5 | 0 | Trigonal bipyramidal / 三角双锥形 | 90°, 120° | PCl₅ |
| 6 | 0 | Octahedral / 八面体形 | 90° | SF₆ |
To work out shape, draw a dot-and-cross diagram to count the total number of electron pairs (bonding + lone), then deduce the arrangement and replace bonding pairs with atoms.
要推断形状，先画出点叉图统计电子对总数（键对+孤对），然后根据电子对排布将键对替换为原子即可。
11. Key Organic Chemistry Concepts | 有机化学核心概念
Organic chemistry in Year 12 OCR focuses on the functional groups, nomenclature, and characteristic reactions of alkanes, alkenes, alcohols, haloalkanes, and basic organic synthesis.
Year 12 OCR 有机化学重点涵盖官能团、命名以及烷烃、烯烃、醇、卤代烷的特征反应，以及基础的有机合成路线。
Homologous series: a family of compounds with the same general formula, similar chemical properties, and a gradation of physical properties (e.g. alkanes CnH2n+2). Functional group determines the chemistry of a molecule.
同系物：具有相同通式、相似化学性质且物理性质呈规律性变化的一族化合物（如烷烃 CnH2n+2）。官能团决定了分子的化学性质。
Reaction mechanisms to recall: electrophilic addition for alkenes (with HBr, Br₂, H₂SO₄), free radical substitution for alkanes (with Cl₂ / UV), nucleophilic substitution for haloalkanes (hydrolysis with NaOH, reaction with NH₃ to form amines), and dehydration / oxidation of alcohols.
需要记住的反应历程：烯烃的亲电加成（与 HBr、Br₂、H₂SO₄），烷烃的自由基取代（Cl₂/紫外光），卤代烷的亲核取代（与 NaOH 水解，与 NH₃ 反应生成胺），以及醇的脱水和氧化。
Key concepts for synthesis include the use of reflux, distillation, separation, drying, and determination of percentage yield.
合成中的关键概念包括回流、蒸馏、分离、干燥以及产率测定。
Isomerism: structural isomers (chain, position, functional group) are essential; Year 13 extends to stereoisomerism (E/Z).
异构现象：必须掌握结构异构（碳链异构、位置异构、官能团异构）；立体异构（E/Z）在 Year 13 中深入学习。
12. Spectroscopy and Analytical Techniques | 光谱与分析技术
Infrared (IR) spectroscopy identifies functional groups by absorption of infrared radiation. Bonds vibrate at characteristic frequencies; an absorption peak appears when the bond polarity changes during vibration.
红外（IR）光谱通过吸收红外辐射识别官能团。化学键在特定频率处振动，当振动过程中键的极性改变时，会出现吸收峰。
Key IR absorptions to recognise: O–H in alcohols (broad, 3200–3550 cm⁻¹), C=O in carbonyl compounds (sharp, 1640–1750 cm⁻¹), O–H in carboxylic acids (very broad, 2500–3300 cm⁻¹), C–O (1000–1300 cm⁻¹).
需识别的关键 IR 吸收峰：醇中的 O–H（宽峰，3200–3550 cm⁻¹），羰基化合物中的 C=O（尖峰，1640–1750 cm⁻¹），羧酸中的 O–H（非常宽的峰，2500–3300 cm⁻¹），C–O（1000–1300 cm⁻¹）。
Mass spectrometry determines relative molecular mass and structural features. The molecular ion peak M⁺ gives the Mr of the compound. Fragmentation produces smaller ions; the base peak is the most intense peak (set to 100%).
质谱用于测定相对分子质量与结构特征。分子离子峰 M⁺ 给出化合物的 Mr。碎裂产生较小的离子；基峰是强度最大的峰（设为 100%）。
The M+1 peak arises from ¹³C isotope (about 1.1% natural abundance per carbon atom), helping to confirm the number of carbon atoms.
M+1 峰来源于 ¹³C 同位素（每有一个碳原子，天然丰度约 1.1%），可用于确认碳原子数目。
Fragmentation patterns can be predicted by breaking bonds in the molecular ion; common fragments include m/z = 15 (CH₃⁺), 29 (C₂H₅⁺), 43 (C₃H₇⁺) etc. for alkanes.
碎裂规律可通过分子离子中的键断裂来预测；常见碎片如烷烃的 m/z = 15 (CH₃⁺)、29 (C₂H₅⁺)、43 (C₃H₇⁺) 等。
Combined use of IR and mass spectrometry, along with elemental analysis, allows full structural determination of organic compounds.
联合使用红外、质谱以及元素分析，可以完成有机化合物的结构测定。
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